Finite Group Databasebeta

← C3×#10608038 #14329518

Subgroups — C3×#10608038 #14329518

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4082C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic
5C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6C3×#65263C211yesmaximal, characteristic, complemented
7C3×#65235C212yesmaximal, complemented
8C3×#65234C212yesmaximal, complemented
9C3×#65233C212yesmaximal, complemented
10C3×C22⋊C4×Dic5C212yesmaximal, complemented
11C3×C4×#683C211yesmaximal, characteristic, complemented
12#10608038C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×Dic5C2212yes—
15C22×C3×Dic10C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2212yes—
18C2×C3×C5×C22⋊C4C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C3×C22⋊Dic5C2212yes—
21C2×C3×C22⋊Dic5C2212yes—
22C2×C3×C22⋊Dic5C2212yes—
23C3×#4082C418yescomplemented
24C3×D4×Dic5—24no—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×#683C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2212yes—
31C2×C3×C4×Dic5C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×C4×Dic10—24no—
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2367—51nomaximal, Hall
40C2×#4082C2×C311yescharacteristic
41C2×D4×Dic5C2×C311yescharacteristic
42C2×C4×Dic10C2×C311yescharacteristic, complemented
43C5×#390C2×C311yescharacteristic
44C4⋊C4×Dic5C2×C311yescharacteristic, complemented
45#65263C2×C311yescharacteristic, complemented
46#65235C2×C312yescomplemented
47#65234C2×C312yescomplemented
48#65233C2×C312yescomplemented
49C22⋊C4×Dic5C2×C312yescomplemented
50C4×#683C2×C311yescharacteristic, complemented
51C24×C3×C5C2312yes—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4C2×C414yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×Dic5—24no—
60C22×C3×Dic5—24no—
61C22×C3×Dic5—42no—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2311yescharacteristic
68C2×C3×Dic10—22no—
69C2×C3×Dic10—22no—
70C2×C3×Dic10C2×C414yescomplemented
71C3×C5×C4⋊C4—22no—
72C3×C5×C22⋊C4—24no—
73C3×C5×C22⋊C4—42no—
74C3×C42×C5—22no—
75C3×C22⋊Dic5—24no—
76C3×C22⋊Dic5C2×C418yescomplemented
77C3×C22⋊Dic5C2×C418yescomplemented
78C3×C4⋊Dic5D414yes—
79C3×#683—22no—
80C3×#683—24no—
81C3×#683—22no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5—24no—
84C3×C4×Dic5—42no—
85C3×C4×Dic5C2×C414yescomplemented
86C2×C3×#124—51no—
87C2×C3×C4×Q8—51no—
88C2×C3×C4×D4—51no—
89C3×#391—51no—
90C3×#390D511yescharacteristic
91C3×#388—52no—
92C3×#388—52no—
93C3×#385—52no—
94C3×C4×C4⋊C4—51no—
95C3×C4×C4⋊C4—51no—
96C3×C4×C22⋊C4—52no—
97C22×C5×D4C22×C311yescharacteristic
98C23×Dic5C22×C312yes—
99C22×Dic10C22×C311yescharacteristic
100C2×C5×C4⋊C4C22×C311yescharacteristic
101C2×C5×C22⋊C4C22×C312yes—
102C2×C5×C22⋊C4C22×C312yes—
103C2×C42×C5C22×C311yescharacteristic
104C2×C22⋊Dic5C22×C312yes—
105C2×C22⋊Dic5C22×C312yes—
106C2×C22⋊Dic5C22×C312yes—
107#4082C3×C418yescomplemented
108D4×Dic5—24no—
109C2×C4⋊Dic5C22×C311yescharacteristic
110C2×#683C22×C312yes—
111C2×#683C22×C311yescharacteristic
112C2×#683C22×C311yescharacteristic
113C2×C4×Dic5C22×C312yes—
114C2×C4×Dic5C22×C311yescharacteristic
115C2×C4×Dic5C22×C312yes—
116C2×C4×Dic5C22×C311yescharacteristic
117C4×Dic10—24no—
118#3963C22×C311yescharacteristic
119#3963C22×C311yescharacteristic
120#3963C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#2367—51noSylow
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5C22×C414yes—
131C23×C3×C5C2411yescharacteristic
132C3×C5×D4—28no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5#4112yes—
144C2×C3×C4×C5#4112yes—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—48no—
159C2×C3×Dic5C22×C412yes—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C414yes—
162C2×C3×Dic5C2×D414yes—
163C2×C3×Dic5#4112yes—
164C3×Dic10—28no—
165C22×C3×Q8—51no—
166C22×C3×D4C2×D511yescharacteristic
167C23×C3×C4—52no—
168C3×#124—58no—
169C3×C4×Q8—104no—
170C3×C4×D4—104no—
171C2×C3×C4⋊C4—51no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C4⋊C4—51no—
174C2×C3×C4⋊C4—52no—
175C2×C3×C4⋊C4C2×D511yescharacteristic
176C2×C3×C22⋊C4—52no—
177C2×C3×C22⋊C4—52no—
178C2×C3×C22⋊C4—52no—
179C2×C3×C22⋊C4C2×D512yes—
180C2×C3×C22⋊C4C2×D512yes—
181C2×C3×C42—51no—
182C2×C3×C42—52no—
183C2×C3×C42—51no—
184C2×C3×C42—52no—
185C2×C3×C42C2×D511yescharacteristic
186C3×#95—51no—
187C3×#95—52no—
188C3×#95—52no—
189C3×#95—51no—
190C3×#95—52no—
191C24×C5C23×C312yes—
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4C2×C3×C414yes—
195C22×C4×C5C23×C311yescharacteristic
196C22×C4×C5C23×C312yes—
197C22×C4×C5C23×C311yescharacteristic
198C22×C4×C5C23×C311yescharacteristic
199C22×Dic5—24no—
200C22×Dic5—24no—
201C22×Dic5—42no—
202C22×Dic5C23×C311yescharacteristic
203C22×Dic5C23×C312yes—
204C22×Dic5C23×C311yescharacteristic
205C22×Dic5C23×C311yescharacteristic
206C22×Dic5C23×C312yes—
207C22×Dic5C23×C311yescharacteristic
208C2×Dic10—22no—
209C2×Dic10—22no—
210C2×Dic10C2×C3×C414yescomplemented
211C5×C4⋊C4—22no—
212C5×C22⋊C4—24no—
213C5×C22⋊C4—42no—
214C42×C5—22no—
215C22⋊Dic5—24no—
216C22⋊Dic5C2×C3×C418yescomplemented
217C22⋊Dic5C2×C3×C418yescomplemented
218C4⋊Dic5C3×D414yes—
219#683—22no—
220#683—24no—
221#683—22no—
222C4×Dic5—22no—
223C4×Dic5—24no—
224C4×Dic5—42no—
225C4×Dic5C2×C3×C414yescomplemented
226C2×#124—51no—
227C2×C4×Q8—51no—
228C2×C4×D4—51no—
229#391—51no—
230#390C3×D511yescharacteristic
231#388—52no—
232#388—52no—
233#385—52no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
236C4×C22⋊C4—52no—
237C22×C3×C5—24no—
238C22×C3×C5—24no—
239C22×C3×C5—24no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5—42no—
244C22×C3×C5C23×C411yescharacteristic
245C22×C3×C5C22×D411yescharacteristic
246C22×C3×C5C2×#4111yescharacteristic
247C22×C3×C5C2×#4111yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5H(5,𝔽2)11yescharacteristic
250C22×C3×C52−1+411yescharacteristic
251C3×C4×C5—22no—
252C3×C4×C5—41no—
253C3×C4×C5—42no—
254C3×C4×C5C4×D414yes—
255C3×Dic5—24no—
256C3×Dic5—22no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C3×Dic5—24no—
260C3×Dic5—41no—
261C24×C3C22×D512yes—
262C2×C3×Q8—54no—
263C2×C3×Q8—102no—
264C2×C3×Q8—102no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4C4×D514yes—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—52no—
272C22×C3×C4—52no—
273C22×C3×C4—51no—
274C22×C3×C4—104no—
275C22×C3×C4—104no—
276C22×C3×C4—202no—
277C22×C3×C4C22×D512yes—
278C22×C3×C4C22×D511yescharacteristic
279C22×C3×C4C22×D511yescharacteristic
280C22×C3×C4C22×D511yescharacteristic
281C3×C4⋊C4—22no—
282C3×C4⋊C4—54no—
283C3×C4⋊C4—102no—
284C3×C4⋊C4—104no—
285C3×C4⋊C4—102no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—58no—
289C3×C22⋊C4—58no—
290C3×C22⋊C4—104no—
291C3×C42—22no—
292C3×C42—54no—
293C3×C42—104no—
294C3×C42—102no—
295C3×C42—202no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5C22×C3×C414yes—
303C23×C5C24×C311yescharacteristic
304C5×D4—28no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5C22×C3×C412yes—
314C2×C4×C5C2×C3×D412yes—
315C2×C4×C5C3×#4112yes—
316C2×C4×C5C3×#4112yes—
317C2×Dic5—22no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—21no—
324C2×Dic5—22no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—48no—
331C2×Dic5C22×C3×C412yes—
332C2×Dic5C22×C3×C412yes—
333C2×Dic5C22×C3×C414yes—
334C2×Dic5C2×C3×D414yes—
335C2×Dic5C3×#4112yes—
336Dic10—28no—
337C22×Q8—51no—
338C22×D4C2×C3×D511yescharacteristic
339C23×C4—52no—
340#124—58no—
341C4×Q8—104no—
342C4×D4—104no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—52no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4C2×C3×D511yescharacteristic
348C2×C22⋊C4—52no—
349C2×C22⋊C4—52no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4C2×C3×D512yes—
352C2×C22⋊C4C2×C3×D512yes—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—52no—
356C2×C42—52no—
357C2×C42C2×C3×D511yescharacteristic
358#95—51no—
359#95—52no—
360#95—52no—
361#95—51no—
362#95—52no—
363C2×C3×C5—44no—
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5C4×#4111yescharacteristic
366C2×C3×C5#52011yescharacteristic
367C2×C3×C5#54611yescharacteristic
368C2×C3×C5#54811yescharacteristic
369C2×C3×C5#55611yescharacteristic
370C2×C3×C5#55911yescharacteristic
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3C2×C4×D514yes—
378C23×C3C23×D511yescharacteristic
379C3×Q8—108no—
380C3×D4—28no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—52no—
390C2×C3×C4—52no—
391C2×C3×C4—54no—
392C2×C3×C4—54no—
393C2×C3×C4—52no—
394C2×C3×C4—102no—
395C2×C3×C4—101no—
396C2×C3×C4—101no—
397C2×C3×C4—102no—
398C2×C3×C4—101no—
399C2×C3×C4—102no—
400C2×C3×C4—101no—
401C2×C3×C4—101no—
402C2×C3×C4—102no—
403C2×C3×C4—101no—
404C2×C3×C4—101no—
405C2×C3×C4—101no—
406C2×C3×C4—101no—
407C2×C3×C4—208no—
408C2×C3×C4C2×C4×D512yes—
409C2×C3×C4D4×D512yes—
410C2×C3×C4#71112yes—
411C2×C3×C4#71112yes—
412C22×C5—24no—
413C22×C5—24no—
414C22×C5—24no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—42no—
418C22×C5—42no—
419C22×C5C23×C3×C411yescharacteristic
420C22×C5C22×C3×D411yescharacteristic
421C22×C5C2×C3×#4111yescharacteristic
422C22×C5C2×C3×#4111yescharacteristic
423C22×C5C2×C3×#4111yescharacteristic
424C22×C5C3×H(5,𝔽2)11yescharacteristic
425C22×C5C3×2−1+411yescharacteristic
426C4×C5—22no—
427C4×C5—42no—
428C4×C5—41no—
429C4×C5C3×C4×D414yes—
430Dic5—24no—
431Dic5—22no—
432Dic5—22no—
433Dic5—22no—
434Dic5—24no—
435Dic5—41no—
436C24C22×C3×D512yes—
437C2×Q8—54no—
438C2×Q8—102no—
439C2×Q8—102no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4C3×C4×D514yes—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—51no—
449C22×C4—104no—
450C22×C4—104no—
451C22×C4—202no—
452C22×C4C22×C3×D512yes—
453C22×C4C22×C3×D511yescharacteristic
454C22×C4C22×C3×D511yescharacteristic
455C22×C4C22×C3×D511yescharacteristic
456C4⋊C4—22no—
457C4⋊C4—54no—
458C4⋊C4—104no—
459C4⋊C4—102no—
460C4⋊C4—102no—
461C22⋊C4—24no—
462C22⋊C4—42no—
463C22⋊C4—58no—
464C22⋊C4—58no—
465C22⋊C4—104no—
466C42—22no—
467C42—54no—
468C42—104no—
469C42—102no—
470C42—202no—
471C3×C5#236711yescharacteristic, complemented, Hall
472C22×C3—24no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×D4×D511yescharacteristic
481C22×C3C2×#71111yescharacteristic
482C22×C3C2×#71111yescharacteristic
483C22×C3#414411yescharacteristic
484C22×C3D5×#4111yescharacteristic
485C22×C3#415011yescharacteristic
486C3×C4—22no—
487C3×C4—41no—
488C3×C4—42no—
489C3×C4—104no—
490C3×C4—102no—
491C3×C4—102no—
492C3×C4—104no—
493C3×C4—102no—
494C3×C4—201no—
495C3×C4#402714yes—
496C2×C5—44no—
497C2×C5C2×C3×C4×D411yescharacteristic
498C2×C5C3×C4×#4111yescharacteristic
499C2×C5C3×#52011yescharacteristic
500C2×C5C3×#54611yescharacteristic
501C2×C5C3×#54811yescharacteristic
502C2×C5C3×#55611yescharacteristic
503C2×C5C3×#55911yescharacteristic
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23C2×C3×C4×D514yes—
511C23C23×C3×D511yescharacteristic
512Q8—108no—
513D4—28no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—52no—
523C2×C4—52no—
524C2×C4—54no—
525C2×C4—54no—
526C2×C4—52no—
527C2×C4—102no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—102no—
531C2×C4—101no—
532C2×C4—102no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—102no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—208no—
541C2×C4C2×C3×C4×D512yes—
542C2×C4C3×D4×D512yes—
543C2×C4C3×#71112yes—
544C2×C4C3×#71112yes—
545C2×C3—44no—
546C2×C3C2×#402711yescharacteristic
547C2×C3C4×#71111yescharacteristic
548C2×C3#6588011yescharacteristic
549C2×C3#6593211yescharacteristic
550C2×C3#6594611yescharacteristic
551C2×C3#6600511yescharacteristic
552C2×C3#6604711yescharacteristic
553C5C3×#236711yescharacteristic, complemented, Sylow
554C22—24no—
555C22—24no—
556C22—24no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22C22×C3×C4×D511yescharacteristic
562C22C2×C3×D4×D511yescharacteristic
563C22C2×C3×#71111yescharacteristic
564C22C2×C3×#71111yescharacteristic
565C22C3×#414411yescharacteristic
566C22C3×D5×#4111yescharacteristic
567C22C3×#415011yescharacteristic
568C4—22no—
569C4—41no—
570C4—42no—
571C4—102no—
572C4—102no—
573C4—102no—
574C4—104no—
575C4—104no—
576C4—201no—
577C4C3×#402714yes—
578C3#1060803811yescharacteristic, direct product factor, Sylow
579C2—44no—
580C2C2×C3×#402711yescharacteristic
581C2C3×C4×#71111yescharacteristic
582C2C3×#6588011yescharacteristic
583C2C3×#6593211yescharacteristic
584C2C3×#6594611yescharacteristic
585C2C3×#6600511yescharacteristic
586C2C3×#6604711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#390C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC3×#390D5
hypocenterC5C3×#2367
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C3×C4×Dic10C2semidirect
5. C3×C4⋊C4×Dic5C2semidirect
6. C3×#65263C2semidirect
7. C3×#65235C2semidirect
8. C3×#65234C2semidirect
9. C3×#65233C2semidirect
10. C3×C22⋊C4×Dic5C2semidirect
11. C3×C4×#683C2semidirect
12. #10608038C3direct (N × H)
23. C3×#4082C4semidirect
42. C2×C4×Dic10C2×C3semidirect
44. C4⋊C4×Dic5C2×C3semidirect
45. #65263C2×C3semidirect
46. #65235C2×C3semidirect
47. #65234C2×C3semidirect
48. #65233C2×C3semidirect
49. C22⋊C4×Dic5C2×C3semidirect
50. C4×#683C2×C3semidirect
70. C2×C3×Dic10C2×C4semidirect
76. C3×C22⋊Dic5C2×C4semidirect
77. C3×C22⋊Dic5C2×C4semidirect
85. C3×C4×Dic5C2×C4semidirect
107. #4082C3×C4semidirect
210. C2×Dic10C2×C3×C4semidirect
216. C22⋊Dic5C2×C3×C4semidirect
217. C22⋊Dic5C2×C3×C4semidirect
225. C4×Dic5C2×C3×C4semidirect
471. C3×C5#2367semidirect
553. C5C3×#2367semidirect
578. C3#10608038direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#40822
C2×C3×D4×Dic52
C2×C3×C4×Dic102
C3×C5×#3902
C3×C4⋊C4×Dic52
C3×#652632
C3×#652352
C3×#652342
C3×#652332
C3×C22⋊C4×Dic52
C3×C4×#6832
#106080383
C3×#23675